All categories

3 years ago

What is the domain and range for the following function and its inverse?

Mathematics

1 answer:

Basile [38]3 years ago

4 0

Answer:

"f(x)

domain: all real numbers, range: all real numbers

f–1(x)

domain: all real numbers, range: all real numbers"

Step-by-step explanation:

We can use the fact that the domain of a function and the range of its inverse are equal.

Also, the range of the function and the domain of its inverse are equal as well.

<em>Looking at the function f(x/ = -x + 5, we see that this is a line with a negative slope of 1 and a y-intercept of +5. </em>

As we know from the graph of lines, there is no restricting values in x and y. So for the original function, domain is the set of all real numbers and the range is the set of all real numbers.

For the inverse, the range is set of all real numbers and domain is also the set of all real numbers.

First answer choice is right.

You might be interested in

Help me! will give brainliest!

lara [203]

Answer:

Step-by-step explanation:

the answer is 1 by 4

we have to bracket of then plus and minus = minus

then we wil minus it and simplify it then we will get our answer

5 0

3 years ago

The bill for dinner was $34. You left $50 to pay for the meal and tip the server. What percent of the meal did you leave as a ti

9966 [12]

Answer:

Step-by-step explanation:

$50 - 34 = 16$

6 0

3 years ago

The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.

solong [7]

Answer:

$20$ .

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are $a$ , $b$ , and $c$ :

$a + b > c$ ,

$a + c > b$ , and

$b + c > a$ .

In this question, the length of the sides are $10$ , $24$ , and $x$ . The length of these sides should satisfty the following inequalities:

$10 + 24 > x$ ,

$10 + x > 24$ , and

$24 + x > 10$ .

Since $x > 0$ , the inequality $24 + x > 10$ is guarenteed to be satisfied.

Simplify $10 + 24 > x$ to obtain the inequality $x < 35$ .

Similarly, simplify $10 + x > 24$ to obtain the inequality $x > 14$ .

Since $x$ needs to be a whole number, the greatest $x$ that satisfies $x < 35$ would be $34$ . Similarly, the least $x\!$ that satisfies $x > 14$ would be $15$ . Thus, $x\!\!$ could be any whole number between $15\!$ and $34\!$ (inclusive.)

There are a total of $34 - 15 + 1 = 20$ distinct whole numbers between $15$ and $34$ (inclusive.) Thus, the number of possible whole number values for $x$ would be $20$ .